Well, it is a good thing that no one is having problems with this little board. Luckily, neither am I. Anyone want my extra one?
The problem ended up being the hard drive.
I bought a external enclosure to put the Mini's drive into so I could get the data off it and it would not work in the enclosure. I had an old 20 GB drive laying around so I put that in the Mini and *boom*, it worked! Some thing in the drive was keeping the computer from working at all. No resetting the PRAM, booting from CD, booting from an external drive, nothing.
So, I went out and picked up a 80 GB Western Digital and it is working perfectly.
Now, should I call the Apple Store Genius and tell him what was wrong with it so they can possibly diagnose someone else's Mini in the future?